Triangle Congruence Criteria Reference
About This Reference
This comprehensive reference shows all five valid triangle congruence criteria and two common invalid cases, providing a quick visual guide for identifying which criterion applies.
Valid Criteria (Green)
| Criterion | Full Name | What's Needed |
|---|---|---|
| SSS | Side-Side-Side | Three pairs of congruent sides |
| SAS | Side-Angle-Side | Two sides + included angle |
| ASA | Angle-Side-Angle | Two angles + included side |
| AAS | Angle-Angle-Side | Two angles + non-included side |
| HL | Hypotenuse-Leg | Right triangles: hypotenuse + one leg |
Invalid Criteria (Red)
| Criterion | Why It Fails |
|---|---|
| AAA | Creates similar triangles, not congruent (different sizes possible) |
| SSA | Ambiguous case - two different triangles can have same SSA |
Visual Markers
- Tick marks on sides indicate congruent sides (1, 2, or 3 ticks)
- Arc marks at vertices indicate congruent angles
- Right angle squares indicate 90° angles
Interaction
Click on any criterion panel to highlight it and dim the others. Click again to show all.
Key Terms
- Included angle: The angle formed BETWEEN two sides
- Included side: The side that is BETWEEN two angles
- Hypotenuse: The side opposite the right angle in a right triangle
Learning Objectives
- Remember all five valid congruence criteria
- Understand why AAA and SSA are not valid
- Evaluate which criterion applies in different situations
Bloom's Taxonomy Level
Remembering, Understanding, and Evaluating
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